/// <summary>
/// Return the confidence interval of the population mean (measured on a continuous random variable) given a random sample
///
/// Note that this is for a variable whose values are continuous
/// </summary>
/// <param name="sampleMean">point estimate sample mean given by the random sample</param>
/// <param name="sampleStdDev">point estimate sample standard deviation given by the random sample</param>
/// <param name="sampleSize">size of the random sample</param>
/// <param name="confidence_level"></param>
/// <returns></returns>
public static double[] GetConfidenceInterval(double sampleMean, double sampleStdDev, int sampleSize, double confidence_level, bool useStudentT = false)
{
double standard_error = StandardError.GetStandardError(sampleStdDev, sampleSize);
double[] confidence_interval = new double[2];
double p1 = (1 - confidence_level) / 2.0;
double p2 = 1 - p1;
double critical_value1 = 0;
double critical_value2 = 0;
if (sampleSize < 30 || useStudentT) //if sample size is smaller than 30, then CLT for population statistics such as sample mean no longer holds and Student's t distribution should be used in place of the normal distribution
{
int df = sampleSize - 1;
critical_value1 = StudentT.GetQuantile(p1, df);
critical_value2 = StudentT.GetQuantile(p2, df);
}
else
{
critical_value1 = Gaussian.GetQuantile(p1);
critical_value2 = Gaussian.GetQuantile(p2);
}
confidence_interval[0] = sampleMean + critical_value1 * standard_error;
confidence_interval[1] = sampleMean + critical_value2 * standard_error;
return(confidence_interval);
}
/// <summary>
/// Get the confidence interval for the difference between two classes
///
/// Note that this is for variables with continuous values
/// </summary>
/// <param name="sample_for_var1">random sample drawn for class 1</param>
/// <param name="sample_for_var2">random sample drawn for class 2</param>
/// <param name="confidence_level">confidencen level</param>
/// <returns>The confidence interval for the difference between two classes in the population given the confidence level</returns>
public static double[] GetConfidenceIntervalForDiff(double[] sample_for_var1, double[] sample_for_var2, double confidence_level, bool useStudentT = false, double correlation = 0)
{
double point_estimate, SE;
LinearCombination.Diff(sample_for_var1, sample_for_var2, correlation, out point_estimate, out SE);
double p1 = (1 - confidence_level) / 2;
double p2 = 1 - p1;
double critical_value1 = 0;
double critical_value2 = 0;
if (sample_for_var1.Length < 30 || sample_for_var2.Length < 30 || useStudentT) //if sample size is smaller than 30, then CLT for population statistics such as sample mean no longer holds and Student's t distribution should be used in place of the normal distribution
{
int df = System.Math.Min(sample_for_var1.Length - 1, sample_for_var2.Length - 1);
critical_value1 = StudentT.GetQuantile(p1, df);
critical_value2 = StudentT.GetQuantile(p2, df);
}
else
{
critical_value1 = Gaussian.GetQuantile(p1);
critical_value2 = Gaussian.GetQuantile(p2);
}
return(new double[] { point_estimate + critical_value1 * SE, point_estimate + critical_value2 * SE });
}
/// <summary>
/// Return the confidence interval of the population mean at a given confidence level, given the point estimate sample mean are known from multiple groups / classes
///
/// Note that each class should be a continuous variable.
/// </summary>
/// <param name="sampleMeans">point estimate sample means from different groups/classes</param>
/// <param name="sampleStdDev">point estimate sample standard deviations from different groups / classes</param>
/// <param name="sampleSizes">sample size from different classes</param>
/// <param name="confidence_level">The given confidence level</param>
/// <param name="useStudentT">whether student t should be used for test statistic</param>
/// <returns>The confidence level of the population mean at the given confidence level</returns>
public static double[] GetConfidenceInterval(double[] sampleMeans, double[] sampleStdDev, int[] sampleSizes, double confidence_level, bool useStudentT = false)
{
double[] standardErrors = new double[sampleMeans.Length];
for (int i = 0; i < sampleMeans.Length; ++i)
{
standardErrors[i] = StandardError.GetStandardError(sampleStdDev[i], sampleSizes[i]);
}
double standardError = StandardError.GetStandardErrorForWeightAverages(sampleSizes, standardErrors);
double sampleMean = Mean.GetMeanForWeightedAverage(sampleMeans, sampleSizes);
double p1 = (1 - confidence_level) / 2.0;
double p2 = 1 - p1;
bool shouldUseStudentT = useStudentT;
if (!shouldUseStudentT)
{
for (int i = 0; i < sampleSizes.Length; ++i)
{
if (sampleSizes[i] < 30)
{
shouldUseStudentT = true;
break;
}
}
}
double critical_value1 = 0;
double critical_value2 = 0;
if (shouldUseStudentT)
{
int smallestSampleSize = int.MaxValue;
for (int i = 0; i < sampleSizes.Length; ++i)
{
if (sampleSizes[i] < smallestSampleSize)
{
smallestSampleSize = sampleSizes[i];
}
}
int df = smallestSampleSize - 1;
critical_value1 = StudentT.GetQuantile(p1, df);
critical_value2 = StudentT.GetQuantile(p2, df);
}
else
{
critical_value1 = Gaussian.GetQuantile(p1);
critical_value2 = Gaussian.GetQuantile(p2);
}
double[] confidence_interval = new double[2];
confidence_interval[0] = sampleMean + critical_value1 * standardError;
confidence_interval[1] = sampleMean + critical_value2 * standardError;
return(confidence_interval);
}